355 research outputs found
Remote State Estimation with Smart Sensors over Markov Fading Channels
We consider a fundamental remote state estimation problem of discrete-time
linear time-invariant (LTI) systems. A smart sensor forwards its local state
estimate to a remote estimator over a time-correlated -state Markov fading
channel, where the packet drop probability is time-varying and depends on the
current fading channel state. We establish a necessary and sufficient condition
for mean-square stability of the remote estimation error covariance as
, where denotes the
spectral radius, is the state transition matrix of the LTI system,
is a diagonal matrix containing the packet drop probabilities in
different channel states, and is the transition probability matrix
of the Markov channel states. To derive this result, we propose a novel
estimation-cycle based approach, and provide new element-wise bounds of matrix
powers. The stability condition is verified by numerical results, and is shown
more effective than existing sufficient conditions in the literature. We
observe that the stability region in terms of the packet drop probabilities in
different channel states can either be convex or concave depending on the
transition probability matrix . Our numerical results suggest that
the stability conditions for remote estimation may coincide for setups with a
smart sensor and with a conventional one (which sends raw measurements to the
remote estimator), though the smart sensor setup achieves a better estimation
performance.Comment: The paper has been accepted by IEEE Transactions on Automatic
Control. Copyright may be transferred without notice, after which this
version may no longer be accessibl
Consensus and Products of Random Stochastic Matrices: Exact Rate for Convergence in Probability
Distributed consensus and other linear systems with system stochastic
matrices emerge in various settings, like opinion formation in social
networks, rendezvous of robots, and distributed inference in sensor networks.
The matrices are often random, due to, e.g., random packet dropouts in
wireless sensor networks. Key in analyzing the performance of such systems is
studying convergence of matrix products . In this paper, we
find the exact exponential rate for the convergence in probability of the
product of such matrices when time grows large, under the assumption that
the 's are symmetric and independent identically distributed in time.
Further, for commonly used random models like with gossip and link failure, we
show that the rate is found by solving a min-cut problem and, hence, easily
computable. Finally, we apply our results to optimally allocate the sensors'
transmission power in consensus+innovations distributed detection
Sparse and Constrained Stochastic Predictive Control for Networked Systems
This article presents a novel class of control policies for networked control
of Lyapunov-stable linear systems with bounded inputs. The control channel is
assumed to have i.i.d. Bernoulli packet dropouts and the system is assumed to
be affected by additive stochastic noise. Our proposed class of policies is
affine in the past dropouts and saturated values of the past disturbances. We
further consider a regularization term in a quadratic performance index to
promote sparsity in control. We demonstrate how to augment the underlying
optimization problem with a constant negative drift constraint to ensure
mean-square boundedness of the closed-loop states, yielding a convex quadratic
program to be solved periodically online. The states of the closed-loop plant
under the receding horizon implementation of the proposed class of policies are
mean square bounded for any positive bound on the control and any non-zero
probability of successful transmission
Kalman Filtering Over a Packet-Dropping Network: A Probabilistic Perspective
We consider the problem of state estimation of a discrete time process over a packet-dropping network. Previous work on Kalman filtering with intermittent observations is concerned with the asymptotic behavior of E[P_k], i.e., the expected value of the error covariance, for a given packet arrival rate. We consider a different performance metric, Pr[P_k ≤ M], i.e., the probability that P_k is bounded by a given M. We consider two scenarios in the paper. In the first scenario, when the sensor sends its measurement data to the remote estimator via a packet-dropping network, we derive lower and upper bounds on Pr[P_k ≤ M]. In the second scenario, when the sensor preprocesses the measurement data and sends its local state estimate to the estimator, we show that the previously derived lower and upper bounds are equal to each other, hence we are able to provide a closed form expression for Pr[P_k ≤ M]. We also recover the results in the literature when using Pr[P_k ≤ M] as a metric for scalar systems. Examples are provided to illustrate the theory developed in the paper
Distributed averaging over communication networks:Fragility, robustness and opportunities
Distributed averaging, a canonical operation among many natural interconnected systems, has found applications in
a tremendous variety of applied fields, including statistical physics, signal processing, systems and control, communication and social science. As information exchange is a central part of distributed averaging systems, it is of practical as well as theoretical importance to understand various properties/limitations of those systems in
the presence of communication constraints and devise new algorithms
to alleviate those limitations.
We study the fragility of a popular distributed averaging algorithm
when the information exchange among the nodes is limited
by communication delays, fading connections and additive noise.
We show that the otherwise well studied and benign
multi-agent system can generate a collective global complex behavior.
We characterize this behavior, common to many natural and human-made interconnected systems, as a collective hyper-jump diffusion process and as a L\\u27{e}vy flights process in a special case. We further describe the mechanism for its emergence and predict its occurrence, under standard assumptions, by checking the Mean Square instability of a certain part of the system. We show that the strong connectivity property of the network topology guarantees that the complex behavior is global and manifested by all
the agents in the network, even though the source of uncertainty is localized. We provide novel computational analysis of the MS stability index under spatially invariant structures and gain certain qualitative as well as quantitative insights of the system.
We then focus on design of agents\u27 dynamics to increase the robustness of distributed averaging system to topology variations. We provide a general structure of distributed averaging systems where individual agents are modeled by LTI systems. We show the problem of designing agents\u27 dynamics for distributed averaging is equivalent to an minimization problem. In this way, we could use tools from robust control theory to build the distributed averaging system where the design is fully distributed and scalable with the size of the network. It is also shown that the agents could be used in different fixed networks and networks with speical time varying interconnections.
We develop new iterative distributed averaging algorithms which allow
agents to compute the average quantity in the presence of
additive noise and random changing interconnections.
The algorithm relaxes several previous restrictive
assumptions on distributed averaging under
uncertainties, such as diminishing step size rule, doubly
stochastic weights, symmetric link switching styles, etc, and
introduces novel mechanism of network feedback to mitigate effects
of communication uncertainties on information aggregation.
Based on the robust distributed averaging algorithm, we propose continuous as well as discrete time computation models
to solve the distributed optimization problem where the objective function is formed by the summation of convex functions of the same variable.
The algorithm shows faster convergence speed than existing ones and
exhibits robustness to additive noise, which is the main source of limitation on algorithms based on convex mixing.
It is shown that agents with simple dynamics and gradient sensing abilities could collectively solve complicated convex optimization problems. Finally, we generalize this algorithm to build a general framework forconstrained convex optimization problems. This framework is shown to be particularly effective to derive solutions for distributed decision making problems and lead to a systems perspective for convex optimization
Statistical Learning for Analysis of Networked Control Systems over Unknown Channels
Recent control trends are increasingly relying on communication networks and
wireless channels to close the loop for Internet-of-Things applications.
Traditionally these approaches are model-based, i.e., assuming a network or
channel model they are focused on stability analysis and appropriate controller
designs. However the availability of such wireless channel modeling is
fundamentally challenging in practice as channels are typically unknown a
priori and only available through data samples. In this work we aim to develop
algorithms that rely on channel sample data to determine the stability and
performance of networked control tasks. In this regard our work is the first to
characterize the amount of channel modeling that is required to answer such a
question. Specifically we examine how many channel data samples are required in
order to answer with high confidence whether a given networked control system
is stable or not. This analysis is based on the notion of sample complexity
from the learning literature and is facilitated by concentration inequalities.
Moreover we establish a direct relation between the sample complexity and the
networked system stability margin, i.e., the underlying packet success rate of
the channel and the spectral radius of the dynamics of the control system. This
illustrates that it becomes impractical to verify stability under a large range
of plant and channel configurations. We validate our theoretical results in
numerical simulations
On the Value of Linear Quadratic Zero-sum Difference Games with Multiplicative Randomness: Existence and Achievability
We consider a wireless networked control system (WNCS) with multiple
controllers and multiple attackers. The dynamic interaction between the
controllers and the attackers is modeled as a linear quadratic (LQ) zero-sum
difference game with multiplicative randomness induced by the multiple-input
and multiple-output (MIMO) wireless fading channels of the controllers and
attackers. We focus on analyzing the existence and achievability of the value
of the zero-sum game. We first establish a general sufficient and necessary
condition for the existence of the game value. This condition relies on the
solvability of a modified game algebraic Riccati equation (MGARE) under an
implicit concavity constraint, which is generally difficult to verify due to
the intermittent controllability or almost sure uncontrollability caused by the
multiplicative randomness. We then introduce a new positive semidefinite (PSD)
kernel decomposition method induced by multiplicative randomness, through which
we obtain a closed-form tight verifiable sufficient condition. Under the
existence condition, we finally construct a saddle-point policy that is able to
achieve the game value in a certain class of admissible policies. We
demonstrate that the proposed saddle-point policy is backward compatible to the
existing strictly feedback stabilizing saddle-point policy.Comment: 32 pages, 3 figure
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